A novel computational approach to pain perception modelling within a Bayesian framework using quantitative sensory testing

Pain perception can be studied as an inferential process in which prior information influences the perception of nociceptive input. To date, there are no suitable psychophysical paradigms to measure this at an individual level. We developed a quantitative sensory testing paradigm allowing for quantification of the influence of prior expectations versus current nociceptive input during perception. Using a Pavlovian-learning task, we investigated the influence of prior expectations on the belief about the varying strength of association between a painful electrical cutaneous stimulus and a visual cue in healthy subjects (N = 70). The belief in cue-pain associations was examined with computational modelling using a Hierarchical Gaussian Filter (HGF). Prior weighting estimates in the HGF model were compared with the established measures of conditioned pain modulation (CPM) and temporal summation of pain (TSP) assessed by cuff algometry. Subsequent HGF-modelling and estimation of the influence of prior beliefs on perception showed that 70% of subjects had a higher reliance on nociceptive input during perception of acute pain stimuli, whereas 30% showed a stronger weighting of prior expectations over sensory evidence. There was no association between prior weighting estimates and CPM or TSP. The data demonstrates relevant individual differences in prior weighting and suggests an importance of top-down cognitive processes on pain perception. Our new psychophysical testing paradigm provides a method to identify individuals with traits suggesting greater reliance on prior expectations in pain perception, which may be a risk factor for developing chronic pain and may be differentially responsive to learning-based interventions.


Dissociative experiences and anomalous perceptions
To assure that perceptual characteristics described by the HGF modelling are not compromised by potential dissociative experiences and/or experiences of anomalous perceptions, we assessed and analyzed the level of occurrence of such experiences and their potential association with outcomes of quantitative sensory paradigms and HGF modelling.
For this, the Dissociative experience scale (DES) and Cardiff anomalous perception scale (CAPS) were assessed in our study sample 1,2 . The DES-score represents the level of dissociative symptoms and is given in a range from 0 to 100. A score above 30 indicates a high level of reported dissociative experiences 1 . The CAPS represents the level of anomalous perceptions along with their distress, intrusiveness, and frequency. The evaluation yields in subscales for the dimensions distress, intrusiveness, and frequency and a total score. The subscales were calculated as the sum of the ratings on their respective dimension. Nonendorsed experiences were set to a score of 0 for each subscale. The total score was calculated as the sum of the endorsed experiences. The CAPS scores are given in a range from 0 to 32, for the total score, and 0 to 160 for the subscales, respectively 2 .
To investigate any potential effects of reported dissociation and anomalous perceptions in our sample with the key outcomes, a Kendall correlation was conducted for the DES score and the CAPS total scores and its subscales with the outcomes of the quantitative sensory testing paradigms (pre/post, control/test arm MDT; threshold for electrical stimuli determined by the QUEST algorithm, conditioned-pain modulation (CPM) pain detection (PDT) and pain tolerance (PTT) thresholds; temporal summation (TSP)), and the weighting of the prior versus sensory evidence (ν) 3 . p-values were corrected using the Holm-Bonferroni correction method 4 .

Model comparison
In line with literature from previous studies, we compared the performance of the HGF model with the νparameter (weighting of prior and sensory evidence), utilized in this study, to non-Bayesian approaches and "HGF without ν" 5,6 . For this, the behavioral data was fit to a Rescorla-Wagner model, an "HGF without ν" and an "HGF with ν" 7 . The ability of the different models to simulate the participants' behavior was then 3 investigated by reintroducing the estimated parameters to each respective model and by simulating participants' responses. The simulated and observed responses for each participant were compared by calculating the percentage of identical responses. Furthermore, the Matthews correlation coefficient (MCC) was calculated between the simulation and observed datasets 8,9 . We calculated potential difference in averages of identical responses and the MCCs between the three models by an ANOVA analysis.
Additionally, we conducted a random-effects Bayesian model selection, with the protected exceedance probability (PXP) as the comparison measure, to get an idea about which model would be favored regarding the fit to our behavioral data 10 . The PXP represents the probability that a specific model is more frequent in the population of models that are compared during the BMS.

Dissociative experiences and anomalous perception
The mean DES score for our sample was 1.71±1.3, which is clearly under the cutoff value of 30 and the estimated mean score values across the general population of 7.9 and 3.7, as reported by Carlson et al. and Goldner et al., respectively 1,11 . The mean CAPS total and subscale score for distress, intrusiveness and frequency were 10.9±6.3, 26.3±18.4, 28.8±18.9 and 24±17.9, respectively (Fig. S1).
Approximately 14 % of our subjects had scores for CAPS subscales, and 13 % scores in the CAPS total score, that were higher than their respective mean scores of a psychotic inpatients group reported by Bell et al. 2 Correlation analysis of the DES and CAPS scores with the QST outcomes and ν did not show any signs of strong association, with the highest correlation coefficient between the ν and the CAPS frequency and total scores being 0.195 and 0.192, respectively (both with a corrected p-value of 1). Table S1 shows the Kendal correlation coefficients for the selected outcomes with DES and CAPS scores.

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Based on these results, ν does not seem to be a phenomenon mainly associated with traits of dissociation or anomalous perceptions, as no strong correlations could be found. The proportion of subjects scoring high for CAPS seems to be in line with studies from the general population, where 11% report high level of anomalous perceptions that are not distressing or compromising in any way 2,12 .   These results demonstrate a superior performance of the "HGF with ν" and point to a good ability to describe and simulate the learning of our participants in contrast to a non-Bayesian model and without ν.